Person 'A' begins a journey from Punjab to Delhi, driving initially at 120 km/hr. Every 36 minutes, he reduces his driving speed by 5 km/hr. If the distance between Punjab and Delhi is 492 km, calculate the time it will take for 'A' to reach Delhi.

Solution

ATQ, As per the problem, The distance Person 'A' covers in the first 36 minutes is (36/60) × 120 = 72 km In the subsequent 36 minutes, the distance covered is = (36/60) × (120 – 5) = 69 km In the following 36 minutes, the speed reduces by another 5 km/hr, resulting in a distance of= (36/60) × (115 – 5) = 66 km/hr The distance travelled in the intervals of 36 minutes each forms an A.P. = (72, 69, 66…… n)km Where, a = 72, d = (69 – 72) = -3 Therefore, (n/2){2a + (n – 1)d} = 492 Or, (n/2){2 × 72 + (n – 1)(-3)} = 492 Or, 144n – 3n² + 3n = 984 Or, n² – 49n + 328= 0 Or, n² – 8n – 41n + 328 = 0 Or, n(n – 8) – 41(n – 8) = 0 Or, n = 41, 8 However, n = 41 would result in a total time of (41 × 36 = 1476) minutes, which would exceed the distance of 492 km. Thus, the suitable value is (n=8),leading to a total time of 36 × 8 = 288 minutes